{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pickle, fileinput\n",
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ind.citeseer\n",
      "0.141471024426\n",
      "2120\n"
     ]
    }
   ],
   "source": [
    "for graphName in [\"ind.citeseer\"]:\n",
    "    graph = pickle.load(open(graphName + \".graph\", \"rb\"))\n",
    "    ally = np.load(graphName + \".ally\", allow_pickle=True)\n",
    "    allx = np.load(graphName + \".allx\", allow_pickle=True)\n",
    "    ty = np.load(graphName + \".ty\", allow_pickle=True)\n",
    "    tx = np.load(graphName + \".tx\", allow_pickle=True)\n",
    "    y = np.load(graphName + \".y\", allow_pickle=True)\n",
    "    x = np.load(graphName + \".x\", allow_pickle=True)\n",
    "    G = nx.from_dict_of_lists(graph)\n",
    "    print(graphName)\n",
    "    print(nx.average_clustering(G))\n",
    "    print(max(map(lambda S:len(S.nodes), nx.connected_component_subgraphs(G))))\n",
    "    # print(map(nx.average_shortest_path_length, nx.connected_component_subgraphs(G)))\n",
    "    break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "((1000, 7), (1000, 1433))\n",
      "((1708, 7), (1708, 1433))\n",
      "((140, 7), (140, 1433))\n"
     ]
    }
   ],
   "source": [
    "print(ty.shape, tx.shape)\n",
    "print(ally.shape, allx.shape)\n",
    "print(y.shape, x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "18.302692"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(np.sum(allx, axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_index = [int(line.strip()) for line in fileinput.input(files = (\"ind.cora.test.index\"))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0.00714286, 0.02142857, 0.02142857, ..., 0.        , 0.02857143,\n",
       "         0.02857143]], dtype=float32)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(x, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2708"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(list,\n",
       "            {0: [633, 1862, 2582],\n",
       "             1: [2, 652, 654],\n",
       "             2: [1986, 332, 1666, 1, 1454],\n",
       "             3: [2544],\n",
       "             4: [2176, 1016, 2176, 1761, 1256, 2175],\n",
       "             5: [1629, 2546, 1659, 1659],\n",
       "             6: [1416, 1602, 1042, 373],\n",
       "             7: [208],\n",
       "             8: [281, 1996, 269],\n",
       "             9: [2614, 723, 723],\n",
       "             10: [476, 2545],\n",
       "             11: [1655, 1839],\n",
       "             12: [2661, 1001, 1318, 2662],\n",
       "             13: [1810, 1701],\n",
       "             14: [2034, 2075, 158, 2077, 2668],\n",
       "             15: [2367, 1093, 1090, 1271, 1093],\n",
       "             16: [2444, 1632, 970, 2642],\n",
       "             17: [24, 2140, 1316, 1315, 927],\n",
       "             18: [2082, 139, 1786, 1560, 2145],\n",
       "             19: [1939],\n",
       "             20: [1072, 2374, 2375, 2269, 2270],\n",
       "             21: [1043, 2310],\n",
       "             22: [1703, 1702, 2238, 39, 1234],\n",
       "             23: [2159],\n",
       "             24: [1701, 2139, 1636, 17, 2141, 598, 201],\n",
       "             25: [1344, 2011, 1301, 2317],\n",
       "             26: [2454, 2455, 123, 99, 122],\n",
       "             27: [1810, 606, 2360, 2578],\n",
       "             28: [1687],\n",
       "             29: [963, 2645],\n",
       "             30: [1358, 1416, 2162, 697, 2343, 738],\n",
       "             31: [1594],\n",
       "             32: [1973, 279, 518, 1850],\n",
       "             33: [2119, 911, 588, 1051, 2120, 286, 2040, 2121, 698],\n",
       "             34: [1358],\n",
       "             35: [1296, 1913, 895],\n",
       "             36: [1146, 1640, 1505, 2106, 1781, 2094, 1552, 2107],\n",
       "             37: [2427, 1190, 60],\n",
       "             38: [429, 1160, 862, 863, 862],\n",
       "             39: [1634, 1965, 1349, 1532, 1522, 22, 2357],\n",
       "             40: [507, 866, 1364],\n",
       "             41: [1914, 644, 175, 596],\n",
       "             42: [1372, 87],\n",
       "             43: [963, 2399, 2400, 152, 1653, 1530],\n",
       "             44: [1582, 2624, 2701, 2624],\n",
       "             45: [1986, 733, 2303, 1219, 2667, 2668],\n",
       "             46: [2366, 1604],\n",
       "             47: [1579, 163],\n",
       "             48: [598, 1666, 2471, 2205, 1031, 2041, 1662, 714, 2206],\n",
       "             49: [2034, 1666],\n",
       "             50: [1441],\n",
       "             51: [710, 2214, 2215, 2213, 457, 1392],\n",
       "             52: [1467, 2172, 2182, 1139, 1467, 2053],\n",
       "             53: [1358, 1103, 1739],\n",
       "             54: [767, 401],\n",
       "             55: [210,\n",
       "              1983,\n",
       "              787,\n",
       "              2020,\n",
       "              1156,\n",
       "              210,\n",
       "              771,\n",
       "              60,\n",
       "              815,\n",
       "              2021,\n",
       "              323,\n",
       "              651,\n",
       "              1079],\n",
       "             56: [1616, 412, 447, 1849],\n",
       "             57: [2418],\n",
       "             58: [1715],\n",
       "             59: [1358, 1725, 1627, 609, 615, 1287, 2651, 105, 580, 1067],\n",
       "             60: [55, 1527, 37],\n",
       "             61: [1416, 1309, 2162, 2312, 1080],\n",
       "             62: [485],\n",
       "             63: [1322],\n",
       "             64: [1737, 1209, 2616],\n",
       "             65: [1628,\n",
       "              2418,\n",
       "              2419,\n",
       "              543,\n",
       "              619,\n",
       "              1293,\n",
       "              1156,\n",
       "              771,\n",
       "              2418,\n",
       "              2021,\n",
       "              239],\n",
       "             66: [2631],\n",
       "             67: [540, 282, 2628],\n",
       "             68: [1358, 1986, 391],\n",
       "             69: [1013, 1914, 1926, 1351, 604, 1926, 1920, 2189],\n",
       "             70: [441, 2184],\n",
       "             71: [1986, 206, 2691, 2691],\n",
       "             72: [1358, 1103],\n",
       "             73: [1358,\n",
       "              797,\n",
       "              449,\n",
       "              1136,\n",
       "              558,\n",
       "              1723,\n",
       "              1189,\n",
       "              876,\n",
       "              1214,\n",
       "              1745,\n",
       "              1751,\n",
       "              1035,\n",
       "              1214],\n",
       "             74: [1416, 586, 1042, 2155, 544, 2419, 1118, 1517, 2052],\n",
       "             75: [2222, 2223, 2224, 2225, 84, 583],\n",
       "             76: [88, 2018, 2178],\n",
       "             77: [659, 1803],\n",
       "             78: [1418, 1329, 1219],\n",
       "             79: [2097, 603],\n",
       "             80: [257, 2049, 1117],\n",
       "             81: [2180, 347, 527, 423, 423],\n",
       "             82: [1634, 1138],\n",
       "             83: [1520, 2581],\n",
       "             84: [75, 2224, 284, 2223, 2226],\n",
       "             85: [1065, 2487, 2488],\n",
       "             86: [1336, 2034, 429, 2295],\n",
       "             87: [842, 2164, 42],\n",
       "             88: [2010,\n",
       "              130,\n",
       "              76,\n",
       "              2011,\n",
       "              1677,\n",
       "              2012,\n",
       "              2013,\n",
       "              1713,\n",
       "              1658,\n",
       "              1394,\n",
       "              1288,\n",
       "              498,\n",
       "              696,\n",
       "              1882,\n",
       "              851,\n",
       "              743,\n",
       "              2014,\n",
       "              1732,\n",
       "              162,\n",
       "              841,\n",
       "              1494,\n",
       "              1908,\n",
       "              1741,\n",
       "              1174,\n",
       "              1309,\n",
       "              300,\n",
       "              1527,\n",
       "              1847,\n",
       "              815,\n",
       "              2015,\n",
       "              2016,\n",
       "              2017,\n",
       "              1309,\n",
       "              415,\n",
       "              737,\n",
       "              2394,\n",
       "              2178],\n",
       "             89: [1087, 884, 1401, 2463, 1157, 1094, 258, 1653, 1530, 1585],\n",
       "             90: [1358, 817, 155, 156],\n",
       "             91: [2122, 2001, 330, 2001, 2380, 2123, 1046],\n",
       "             92: [898, 1836],\n",
       "             93: [2151, 550, 1495, 950],\n",
       "             94: [1966,\n",
       "              586,\n",
       "              733,\n",
       "              1649,\n",
       "              2490,\n",
       "              586,\n",
       "              195,\n",
       "              2355,\n",
       "              934,\n",
       "              2263,\n",
       "              2357,\n",
       "              934,\n",
       "              675],\n",
       "             95: [1535,\n",
       "              1838,\n",
       "              2200,\n",
       "              2201,\n",
       "              2197,\n",
       "              2199,\n",
       "              2181,\n",
       "              2054,\n",
       "              861,\n",
       "              334,\n",
       "              1303,\n",
       "              734,\n",
       "              736,\n",
       "              2074,\n",
       "              1628,\n",
       "              1602,\n",
       "              693,\n",
       "              456,\n",
       "              2183,\n",
       "              2182,\n",
       "              1580],\n",
       "             96: [2217],\n",
       "             97: [661, 1353],\n",
       "             98: [1521],\n",
       "             99: [123, 2454, 2455, 123, 122, 2604, 26],\n",
       "             100: [1602, 2056],\n",
       "             101: [1358, 281, 1589],\n",
       "             102: [1623, 109, 1878, 1448, 2256, 1251, 1871, 1561],\n",
       "             103: [139, 484, 306, 608, 1790, 1775],\n",
       "             104: [2210, 864, 401, 1065],\n",
       "             105: [1721, 59, 2651, 2476],\n",
       "             106: [2461],\n",
       "             107: [541, 1113, 971, 1650],\n",
       "             108: [2157, 1647, 2209],\n",
       "             109: [1624,\n",
       "              2045,\n",
       "              236,\n",
       "              306,\n",
       "              124,\n",
       "              1769,\n",
       "              289,\n",
       "              2092,\n",
       "              459,\n",
       "              318,\n",
       "              2093,\n",
       "              1772,\n",
       "              1045,\n",
       "              1785,\n",
       "              1337,\n",
       "              102,\n",
       "              1998,\n",
       "              1787,\n",
       "              610,\n",
       "              1789,\n",
       "              1779,\n",
       "              1346,\n",
       "              153,\n",
       "              519,\n",
       "              133,\n",
       "              1805,\n",
       "              426,\n",
       "              563,\n",
       "              2094,\n",
       "              176,\n",
       "              2095,\n",
       "              1661],\n",
       "             110: [1262, 567, 2279, 1161, 1599],\n",
       "             111: [1358, 1169, 2643, 758, 2492, 1762, 758],\n",
       "             112: [1623, 487, 306, 2080],\n",
       "             113: [540, 747, 1884],\n",
       "             114: [2288, 610, 2506],\n",
       "             115: [973],\n",
       "             116: [1076, 1501],\n",
       "             117: [259, 2537],\n",
       "             118: [1616,\n",
       "              388,\n",
       "              2010,\n",
       "              842,\n",
       "              2030,\n",
       "              446,\n",
       "              255,\n",
       "              1343,\n",
       "              2165,\n",
       "              554,\n",
       "              581,\n",
       "              1690,\n",
       "              1507,\n",
       "              2112,\n",
       "              1029,\n",
       "              2166,\n",
       "              1538,\n",
       "              454,\n",
       "              1851],\n",
       "             119: [646, 1959, 379, 1549, 1901, 1537],\n",
       "             120: [514, 2405, 1842, 483, 816],\n",
       "             121: [1910, 980, 802, 1158, 2251, 589, 2252],\n",
       "             122: [2454, 2455, 99, 26],\n",
       "             123: [2455, 99, 2604, 99, 26],\n",
       "             124: [306, 109, 1367, 1622, 2478],\n",
       "             125: [458, 2363],\n",
       "             126: [1623, 2045, 236, 306, 1551, 2079],\n",
       "             127: [2604],\n",
       "             128: [233, 392, 370, 2270],\n",
       "             129: [441, 701],\n",
       "             130: [88, 2017, 1982],\n",
       "             131: [2169, 834],\n",
       "             132: [904, 1022, 1959, 379, 479],\n",
       "             133: [1623, 2045, 1670, 2082, 1777, 452, 399, 1784, 109],\n",
       "             134: [406],\n",
       "             135: [137, 2144, 2095],\n",
       "             136: [831],\n",
       "             137: [2144, 2329, 2504, 135],\n",
       "             138: [236, 306, 1776],\n",
       "             139: [1623, 660, 103, 1780, 910, 2045, 306, 18],\n",
       "             140: [582, 623, 582],\n",
       "             141: [2034, 1002, 740],\n",
       "             142: [2049, 1628, 525, 2181, 456],\n",
       "             143: [1701, 598, 316],\n",
       "             144: [2192, 1593, 145, 213],\n",
       "             145: [213, 537, 1593, 144, 1165, 2622],\n",
       "             146: [1927, 2059, 897, 1468, 1907],\n",
       "             147: [1976, 1519],\n",
       "             148: [714, 2518, 602, 714, 381, 378, 2518],\n",
       "             149: [1416, 2025, 1655, 1080],\n",
       "             150: [310, 1942, 914],\n",
       "             151: [1986, 2236, 2238, 2335],\n",
       "             152: [2238, 2240, 884, 43],\n",
       "             153: [1623, 2045, 236, 459, 306, 109],\n",
       "             154: [1358,\n",
       "              2525,\n",
       "              1444,\n",
       "              1339,\n",
       "              1238,\n",
       "              1568,\n",
       "              364,\n",
       "              326,\n",
       "              1752,\n",
       "              1753,\n",
       "              1754,\n",
       "              819],\n",
       "             155: [1358, 817, 1736, 90, 1689, 1763, 156],\n",
       "             156: [1358, 817, 90, 1689, 155, 1763],\n",
       "             157: [1701, 598, 1870, 2493],\n",
       "             158: [1701, 2034, 14, 180],\n",
       "             159: [2308, 180],\n",
       "             160: [1986, 745, 277, 743, 2000, 2009, 553],\n",
       "             161: [2010, 842],\n",
       "             162: [88, 323, 1667, 1174, 1268],\n",
       "             163: [47],\n",
       "             164: [210, 211],\n",
       "             165: [598, 1473, 2706, 2707],\n",
       "             166: [271, 2617],\n",
       "             167: [2437, 1056, 168, 2482],\n",
       "             168: [2437, 2438, 167],\n",
       "             169: [1994, 2706],\n",
       "             170: [1358, 1067],\n",
       "             171: [790, 1548, 775],\n",
       "             172: [756, 1692, 2187, 240, 512],\n",
       "             173: [1358, 687, 1033, 1586],\n",
       "             174: [1358, 1742, 629, 2334],\n",
       "             175: [1914, 2388, 955, 596, 41, 2217, 2135],\n",
       "             176: [109, 973, 231],\n",
       "             177: [2679, 2682, 1639, 726],\n",
       "             178: [833],\n",
       "             179: [1986, 231, 197],\n",
       "             180: [159, 2037, 1807, 1020, 2076, 791, 2004, 790, 775, 158],\n",
       "             181: [1013, 1464, 1359, 1683],\n",
       "             182: [183, 997],\n",
       "             183: [1837, 997, 182, 997],\n",
       "             184: [520],\n",
       "             185: [2003, 297],\n",
       "             186: [2702, 1672, 2580, 1228, 1319, 1536, 2580, 1228, 1319],\n",
       "             187: [1208],\n",
       "             188: [1169, 1727],\n",
       "             189: [1072, 1262, 1509, 1509, 564],\n",
       "             190: [2135, 491],\n",
       "             191: [608, 382, 1677, 1998, 2385, 1791],\n",
       "             192: [2472],\n",
       "             193: [441, 458],\n",
       "             194: [1050, 1451, 2646, 1451, 2564, 473],\n",
       "             195: [2424, 94],\n",
       "             196: [429, 2122, 442],\n",
       "             197: [231, 2412, 179, 231],\n",
       "             198: [1255],\n",
       "             199: [1869, 420],\n",
       "             200: [2676, 1439],\n",
       "             201: [1701, 1986, 598, 2430, 570, 297, 24],\n",
       "             202: [1250, 353, 1173, 1345, 1345],\n",
       "             203: [857, 854, 1115, 963, 1869, 854],\n",
       "             204: [415],\n",
       "             205: [1701, 1869],\n",
       "             206: [71, 2691],\n",
       "             207: [833],\n",
       "             208: [7],\n",
       "             209: [2681],\n",
       "             210: [164,\n",
       "              1905,\n",
       "              1614,\n",
       "              1626,\n",
       "              1906,\n",
       "              1907,\n",
       "              55,\n",
       "              1079,\n",
       "              1671,\n",
       "              55,\n",
       "              2309],\n",
       "             211: [164, 356, 1394, 1908, 1909],\n",
       "             212: [1290],\n",
       "             213: [2192, 1593, 145, 144],\n",
       "             214: [2194],\n",
       "             215: [1701, 1986, 2045],\n",
       "             216: [1701, 1542],\n",
       "             217: [2473, 2474, 243],\n",
       "             218: [733,\n",
       "              482,\n",
       "              2119,\n",
       "              1382,\n",
       "              1020,\n",
       "              2076,\n",
       "              792,\n",
       "              1348,\n",
       "              781,\n",
       "              2594,\n",
       "              2091],\n",
       "             219: [1413, 1542, 507],\n",
       "             220: [913, 376, 817],\n",
       "             221: [817],\n",
       "             222: [821],\n",
       "             223: [1761, 1154, 744],\n",
       "             224: [1810, 2034],\n",
       "             225: [2255],\n",
       "             226: [1701],\n",
       "             227: [883, 534],\n",
       "             228: [1358, 1871, 1721, 322, 848],\n",
       "             229: [1894, 1053, 1405, 2118, 1053],\n",
       "             230: [1810, 549, 577, 1095, 1217],\n",
       "             231: [1701, 387, 232, 179, 2217, 197, 551, 232, 1868, 176, 197],\n",
       "             232: [1701, 1986, 869, 231, 231, 1864],\n",
       "             233: [128],\n",
       "             234: [610, 2591],\n",
       "             235: [1701],\n",
       "             236: [1072,\n",
       "              2045,\n",
       "              138,\n",
       "              1572,\n",
       "              2046,\n",
       "              2078,\n",
       "              126,\n",
       "              2079,\n",
       "              153,\n",
       "              306,\n",
       "              109,\n",
       "              306],\n",
       "             237: [2539],\n",
       "             238: [1828],\n",
       "             239: [2182,\n",
       "              1376,\n",
       "              1274,\n",
       "              619,\n",
       "              1069,\n",
       "              1220,\n",
       "              887,\n",
       "              2418,\n",
       "              65,\n",
       "              1759,\n",
       "              1909,\n",
       "              910,\n",
       "              2021],\n",
       "             240: [756, 1472, 512, 1692, 172],\n",
       "             241: [1441],\n",
       "             242: [1131, 279, 2280, 838],\n",
       "             243: [217, 473, 2647, 2648, 2474],\n",
       "             244: [1358, 1072, 565, 1610],\n",
       "             245: [782, 1162],\n",
       "             246: [1358, 1687, 936, 2515],\n",
       "             247: [2583],\n",
       "             248: [1964, 1264, 1531],\n",
       "             249: [1978, 1884, 621],\n",
       "             250: [2429],\n",
       "             251: [1413, 1542, 507, 1300, 1933, 1413, 253, 812],\n",
       "             252: [1973, 711, 973, 2485],\n",
       "             253: [1413, 507, 251],\n",
       "             254: [507, 1211],\n",
       "             255: [118, 1343, 2112, 1266],\n",
       "             256: [756],\n",
       "             257: [80, 2180, 1388, 964],\n",
       "             258: [1240, 963, 89, 2645, 1094, 1153, 1401],\n",
       "             259: [117, 2537],\n",
       "             260: [365],\n",
       "             261: [1701, 873, 1894, 1479],\n",
       "             262: [1464, 1351],\n",
       "             263: [1103, 364, 732],\n",
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       "             265: [1441],\n",
       "             266: [578, 2227, 2229, 809],\n",
       "             267: [670, 2000, 2373, 2373],\n",
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       "             270: [279, 2280, 1195, 1215, 838],\n",
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       "             272: [2012],\n",
       "             273: [374, 846],\n",
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       "             275: [1967, 805],\n",
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       "             277: [973, 160, 553, 1869, 696],\n",
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       "             332: [2, 2615, 665, 2003, 2122],\n",
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       "             336: [1944, 1950],\n",
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       "             379: [1898, 119, 904, 1022, 1959, 1959, 132],\n",
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       "             381: [148, 2518, 2538, 2518],\n",
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       "             384: [1623, 1624],\n",
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       "             389: [1483, 704, 2450, 1743, 1077, 344, 905, 359],\n",
       "             390: [1108],\n",
       "             391: [1986, 2365, 493, 68],\n",
       "             392: [1415, 1825, 720, 1619, 2269, 128],\n",
       "             393: [739],\n",
       "             394: [1063, 577, 2351, 849, 1064],\n",
       "             395: [2367, 640, 1147],\n",
       "             396: [1988, 1217],\n",
       "             397: [2329, 879, 665, 1096],\n",
       "             398: [730, 2177],\n",
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       "             400: [1354],\n",
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       "             402: [1413, 1542, 507, 776, 1940, 1932, 1936],\n",
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       "             404: [1476, 1170],\n",
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       "             411: [1488, 1096, 1577, 2609],\n",
       "             412: [1616, 1849, 56],\n",
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       "              2182,\n",
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       "             422: [545],\n",
       "             423: [525, 347, 315, 527, 81, 81],\n",
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       "             425: [2466],\n",
       "             426: [306, 109, 1805, 1782, 1777, 1789, 487, 1772],\n",
       "             427: [565, 1528],\n",
       "             428: [2248, 368, 2671, 1257, 996],\n",
       "             429: [2043,\n",
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       "             430: [2130],\n",
       "             431: [2694, 2695],\n",
       "             432: [1597, 1442],\n",
       "             433: [436, 756],\n",
       "             434: [1524, 1693, 2408, 2133, 1117],\n",
       "             435: [733, 1912, 486],\n",
       "             436: [1977,\n",
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       "              878,\n",
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       "              1332,\n",
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       "              483,\n",
       "              1980,\n",
       "              1981,\n",
       "              1982,\n",
       "              1131],\n",
       "             437: [1985, 1495, 950, 718, 498],\n",
       "             438: [1983, 787, 1984, 1985, 718, 1667],\n",
       "             439: [1169, 1642],\n",
       "             440: [1296, 2179, 441, 725, 1913, 895],\n",
       "             441: [440, 1537, 344, 671, 70, 1455, 2184, 129, 193, 2094, 454],\n",
       "             442: [627, 196, 2362, 588, 1051, 2120, 286, 698],\n",
       "             443: [1966, 1010, 1531, 1264],\n",
       "             444: [582, 488, 623, 515, 2289, 2290, 2464, 2289, 2290, 828],\n",
       "             445: [1434, 909],\n",
       "             446: [903, 118, 1507],\n",
       "             447: [1616, 1849, 56, 2638],\n",
       "             448: [1824, 1902, 1826, 472],\n",
       "             449: [1834, 73, 1280, 2581],\n",
       "             450: [1569, 2538],\n",
       "             451: [671, 935, 2285],\n",
       "             452: [1623, 133, 306, 1258],\n",
       "             453: [2305, 1806, 2306],\n",
       "             454: [441,\n",
       "              973,\n",
       "              2188,\n",
       "              2189,\n",
       "              1441,\n",
       "              1917,\n",
       "              2190,\n",
       "              581,\n",
       "              2022,\n",
       "              118,\n",
       "              1661],\n",
       "             455: [2486, 2147, 1664],\n",
       "             456: [525, 2054, 95, 667, 2347, 2199, 142, 2472, 544, 1580],\n",
       "             457: [51, 2216, 1201, 2215],\n",
       "             458: [125, 1122, 1953, 1555, 1276, 193],\n",
       "             459: [1623, 153, 109, 1681],\n",
       "             460: [1986, 1989, 2532],\n",
       "             461: [2309, 1203],\n",
       "             462: [1048],\n",
       "             463: [1964, 1703, 1702, 1966],\n",
       "             464: [2444, 2445, 403, 1758],\n",
       "             465: [1403, 896, 349, 1869, 2304],\n",
       "             466: [1358, 2546, 970, 1738, 1305],\n",
       "             467: [1701, 1708, 1172],\n",
       "             468: [647, 1311, 1313],\n",
       "             469: [2412, 2304, 620],\n",
       "             470: [857, 854, 1115, 652, 1097],\n",
       "             471: [1013, 2394, 2013],\n",
       "             472: [1825, 559, 448, 264, 844, 1183, 1182, 2029],\n",
       "             473: [1575, 194, 243, 2647],\n",
       "             474: [1181],\n",
       "             475: [2219, 2219],\n",
       "             476: [1986, 306, 1140, 10, 1800, 1140],\n",
       "             477: [380, 2569, 930, 2569],\n",
       "             478: [514, 2024, 1978],\n",
       "             479: [132, 1880],\n",
       "             480: [598, 687, 2359, 1710, 2359, 2372, 1426],\n",
       "             481: [1810, 2291, 823, 1287],\n",
       "             482: [2230, 1812, 1814, 1807, 2307, 2308, 218, 790, 1810],\n",
       "             483: [436, 2405, 120, 816],\n",
       "             484: [542, 2081, 2046, 1699, 103, 1367, 1775],\n",
       "             485: [1042, 839, 2219, 62],\n",
       "             486: [2077, 435, 2667, 2668],\n",
       "             487: [655,\n",
       "              112,\n",
       "              2026,\n",
       "              1773,\n",
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       "              2080,\n",
       "              1705,\n",
       "              859,\n",
       "              306,\n",
       "              1782,\n",
       "              426,\n",
       "              1772],\n",
       "             488: [444, 2547],\n",
       "             489: [1358, 2390, 2391],\n",
       "             490: [1973, 2105, 1879, 826, 2099, 1309, 1463, 1981, 1131],\n",
       "             491: [190],\n",
       "             492: [1257, 956, 1533, 688, 2678, 2673, 2538],\n",
       "             493: [1759, 1244, 391],\n",
       "             494: [2614],\n",
       "             495: [2192, 1328, 1327],\n",
       "             496: [711, 596, 992],\n",
       "             497: [2419],\n",
       "             498: [1652, 436, 437, 88, 323, 356],\n",
       "             499: [2457, 2458],\n",
       "             500: [2241],\n",
       "             501: [1358, 1765],\n",
       "             502: [279, 1976, 285],\n",
       "             503: [1692, 576, 2001],\n",
       "             504: [1973, 2394, 2396],\n",
       "             505: [573,\n",
       "              1180,\n",
       "              1304,\n",
       "              1448,\n",
       "              1258,\n",
       "              843,\n",
       "              1251,\n",
       "              1779,\n",
       "              1560,\n",
       "              2083,\n",
       "              406],\n",
       "             506: [1013, 1914, 1918, 1352],\n",
       "             507: [219,\n",
       "              1940,\n",
       "              1931,\n",
       "              1211,\n",
       "              1363,\n",
       "              1941,\n",
       "              402,\n",
       "              1933,\n",
       "              1413,\n",
       "              1176,\n",
       "              1300,\n",
       "              253,\n",
       "              254,\n",
       "              251,\n",
       "              812,\n",
       "              1936,\n",
       "              40,\n",
       "              2508],\n",
       "             508: [2325],\n",
       "             509: [1101, 2146, 2148],\n",
       "             510: [1013, 1131, 1171],\n",
       "             511: [1810, 549],\n",
       "             512: [756, 1472, 240, 1692, 172],\n",
       "             513: [565, 1528, 657],\n",
       "             514: [1978, 120, 1882, 1314, 478],\n",
       "             515: [444, 2464, 623, 2547, 2465, 1102, 1102],\n",
       "             516: [2104, 1882],\n",
       "             517: [2105, 952],\n",
       "             518: [666, 32, 2423, 1373],\n",
       "             519: [2045,\n",
       "              387,\n",
       "              1574,\n",
       "              1670,\n",
       "              416,\n",
       "              836,\n",
       "              1998,\n",
       "              1986,\n",
       "              1346,\n",
       "              306,\n",
       "              109,\n",
       "              598],\n",
       "             520: [184],\n",
       "             521: [598],\n",
       "             522: [2097],\n",
       "             523: [429, 949, 2406],\n",
       "             524: [1358, 979, 2476, 1169, 552],\n",
       "             525: [415,\n",
       "              1540,\n",
       "              2180,\n",
       "              2181,\n",
       "              2054,\n",
       "              408,\n",
       "              2182,\n",
       "              142,\n",
       "              423,\n",
       "              347,\n",
       "              1628,\n",
       "              456,\n",
       "              2183,\n",
       "              2057,\n",
       "              2172,\n",
       "              2182],\n",
       "             526: [565, 1742, 1216, 1007],\n",
       "             527: [81, 423],\n",
       "             528: [803],\n",
       "             529: [1419, 1417, 2260, 2260],\n",
       "             530: [1013, 2094, 1505],\n",
       "             531: [606, 2308],\n",
       "             532: [1701, 1863],\n",
       "             533: [1742, 2466],\n",
       "             534: [629, 609, 933, 227],\n",
       "             535: [2641, 2392],\n",
       "             536: [1894, 567],\n",
       "             537: [2192, 1698, 1593, 145, 1165],\n",
       "             538: [1286],\n",
       "             539: [1616, 711, 2155],\n",
       "             540: [1441, 113, 67, 2527, 747],\n",
       "             541: [107, 904, 647, 1896, 1360, 1022],\n",
       "             542: [1623, 484, 306, 1245],\n",
       "             543: [984, 65],\n",
       "             544: [2199, 1769, 2347, 2052, 1580, 74, 399, 456],\n",
       "             545: [422],\n",
       "             546: [1608, 2127, 2127],\n",
       "             547: [1701, 598],\n",
       "             548: [2138, 809, 843, 1937, 1523],\n",
       "             549: [1810, 511, 1497, 230, 1810],\n",
       "             550: [93],\n",
       "             551: [231, 2388],\n",
       "             552: [1358, 1169, 524, 2201],\n",
       "             553: [1995, 366, 1127, 277, 745, 160, 1583, 2009],\n",
       "             554: [306, 118, 685],\n",
       "             555: [1463],\n",
       "             556: [1623, 1805],\n",
       "             557: [1725],\n",
       "             558: [73, 2585, 876, 1706, 1189],\n",
       "             559: [472, 1182, 1579],\n",
       "             560: [2526, 774],\n",
       "             561: [1016],\n",
       "             562: [1483, 1735, 704, 2450],\n",
       "             563: [1701, 2045, 109, 1337, 318, 1337],\n",
       "             564: [1262, 2476, 189],\n",
       "             565: [1398,\n",
       "              513,\n",
       "              244,\n",
       "              1361,\n",
       "              1610,\n",
       "              1723,\n",
       "              1528,\n",
       "              526,\n",
       "              2279,\n",
       "              1038,\n",
       "              427,\n",
       "              687,\n",
       "              1610],\n",
       "             566: [1986, 1907],\n",
       "             567: [760, 536, 1262, 631, 110, 290, 1513],\n",
       "             568: [1810, 1116, 1223, 1223],\n",
       "             569: [1759, 2512],\n",
       "             570: [201, 2430],\n",
       "             571: [696, 1570],\n",
       "             572: [1416, 2025, 2418],\n",
       "             573: [505, 306, 643, 1313, 2407],\n",
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       "             575: [2283],\n",
       "             576: [1810, 665, 2348, 503, 574, 665],\n",
       "             577: [1518,\n",
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       "              2353,\n",
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       "              394,\n",
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       "              1063,\n",
       "              1129],\n",
       "             578: [266, 1879, 1974, 1105],\n",
       "             579: [1808, 994, 1134],\n",
       "             580: [1358, 744, 2444, 1742, 2445, 1758, 1765, 59],\n",
       "             581: [1623, 1792, 1616, 306, 118, 454],\n",
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       "             585: [2526],\n",
       "             586: [1224, 1218, 74, 94, 2155, 94],\n",
       "             587: [1032, 1032],\n",
       "             588: [33, 442, 2383, 698],\n",
       "             589: [1624, 121, 1158, 980],\n",
       "             590: [1954, 1441],\n",
       "             591: [1423, 1017, 1078, 2472, 642],\n",
       "             592: [2669],\n",
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       "             596: [1914, 644, 175, 496, 992, 41],\n",
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       "              1301,\n",
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       "              1100,\n",
       "              165,\n",
       "              2707,\n",
       "              1473],\n",
       "             599: [1271, 1093],\n",
       "             600: [2394],\n",
       "             601: [2229],\n",
       "             602: [148, 378],\n",
       "             603: [2045, 716, 1248, 795, 1821, 79, 1873],\n",
       "             604: [1914, 1652, 1351, 69, 2109],\n",
       "             605: [1107, 2534],\n",
       "             606: [2230, 2360, 1666, 531, 27, 2361],\n",
       "             607: [1213, 1664, 298],\n",
       "             608: [1623, 306, 103, 191, 2080],\n",
       "             609: [1358, 2446, 59, 883, 534, 1041, 2447, 2448],\n",
       "             610: [109, 2287, 2288, 826, 234, 2481, 114],\n",
       "             611: [2690],\n",
       "             612: [2235],\n",
       "             613: [1358, 341],\n",
       "             614: [1475, 2470, 2470, 888],\n",
       "             615: [59, 2443],\n",
       "             616: [1358, 2365, 1739, 2503],\n",
       "             617: [2034, 705],\n",
       "             618: [288, 938],\n",
       "             619: [65, 239],\n",
       "             620: [469, 2534, 923],\n",
       "             621: [2018, 1332, 249, 1978],\n",
       "             622: [1951, 1952, 1002, 886],\n",
       "             623: [444, 584, 2464, 2289, 140, 515],\n",
       "             624: [1042, 1232],\n",
       "             625: [1024],\n",
       "             626: [1358, 372, 2556, 2558],\n",
       "             627: [2122, 2238, 2335, 442],\n",
       "             628: [1764, 1169, 2546, 1725],\n",
       "             629: [174, 883, 534],\n",
       "             630: [973],\n",
       "             631: [567, 2358],\n",
       "             632: [1430],\n",
       "             633: [1701, 0, 1866],\n",
       "             634: [2227, 300],\n",
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       "             641: [2704],\n",
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       "             643: [1538, 573, 1167, 2407],\n",
       "             644: [711, 728, 2177, 596, 41, 1258],\n",
       "             645: [1358,\n",
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       "             648: [1441],\n",
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       "             650: [1250, 1486, 1557, 1685, 1756, 819, 2083],\n",
       "             651: [2023, 1984, 55, 885, 2024, 1667, 2156],\n",
       "             652: [470, 1],\n",
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       "              871,\n",
       "              2523,\n",
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       "             658: [2147],\n",
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       "             661: [1353,\n",
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       "              1880,\n",
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       "              1884,\n",
       "              1885],\n",
       "             662: [932],\n",
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       "             664: [1701],\n",
       "             665: [397, 2120, 576, 2122, 576, 332],\n",
       "             666: [1973, 279, 518, 1850],\n",
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       "             668: [436],\n",
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       "             670: [267, 2606],\n",
       "             671: [2025, 441, 973, 451],\n",
       "             672: [2456, 376],\n",
       "             673: [1986, 1907],\n",
       "             674: [1907],\n",
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       "             679: [1395],\n",
       "             680: [2199],\n",
       "             681: [1986, 1445, 1446, 1171, 1445, 1446],\n",
       "             682: [1224, 973],\n",
       "             683: [2169, 834],\n",
       "             684: [1358, 1282],\n",
       "             685: [554],\n",
       "             686: [1358, 2366],\n",
       "             687: [1358,\n",
       "              1171,\n",
       "              1710,\n",
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       "              290,\n",
       "              1721],\n",
       "             688: [1257, 492],\n",
       "             689: [1358, 1317, 1169, 1721, 1292],\n",
       "             690: [311],\n",
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       "             692: [2629],\n",
       "             693: [2108, 763, 95, 1851, 334],\n",
       "             694: [1478, 2516],\n",
       "             695: [1336, 1681, 1682, 1998, 2319, 1012, 1790, 407, 948],\n",
       "             696: [88, 277, 571, 1570],\n",
       "             697: [30, 1080],\n",
       "             698: [33, 1015, 442, 588, 286],\n",
       "             699: [1701, 2045, 2327],\n",
       "             700: [1691],\n",
       "             701: [735, 739, 129, 2062],\n",
       "             702: [777, 993, 1637, 2101, 1368, 822, 779, 2069, 2070],\n",
       "             703: [2497, 1961, 801],\n",
       "             704: [1483, 969, 562, 389, 2450, 1743, 1412, 2113, 2113],\n",
       "             705: [429, 617],\n",
       "             706: [1240, 2238, 963, 805, 2645],\n",
       "             707: [763],\n",
       "             708: [1358, 2212, 2216, 836],\n",
       "             709: [1896, 1903],\n",
       "             710: [51, 2212, 2213, 1392],\n",
       "             711: [2111, 1285, 496, 539, 252, 414, 2112, 2113, 644],\n",
       "             712: [1464, 850, 2480],\n",
       "             713: [1044],\n",
       "             714: [1385, 148, 148, 48],\n",
       "             715: [2291],\n",
       "             716: [1810, 603, 1821, 2409],\n",
       "             717: [1907],\n",
       "             718: [1416, 438, 437, 2059, 2261],\n",
       "             719: [1623, 1810, 306, 302, 303],\n",
       "             720: [1441, 392, 371],\n",
       "             721: [1034],\n",
       "             722: [1273, 1874, 2500, 1567, 2501, 1567],\n",
       "             723: [2614, 9, 9],\n",
       "             724: [1344, 2394, 2395],\n",
       "             725: [1652, 2071, 440, 1104, 1137],\n",
       "             726: [2671, 1533, 177],\n",
       "             727: [1386, 2570],\n",
       "             728: [1296, 644, 2388, 2553, 1070],\n",
       "             729: [1701, 2534, 1221, 1159, 669],\n",
       "             730: [398],\n",
       "             731: [901, 2199, 1279, 2203],\n",
       "             732: [364, 1756, 2685, 296, 263],\n",
       "             733: [2035,\n",
       "              1062,\n",
       "              1265,\n",
       "              2011,\n",
       "              2301,\n",
       "              2302,\n",
       "              1329,\n",
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       "              1817,\n",
       "              678,\n",
       "              1294,\n",
       "              1818,\n",
       "              401,\n",
       "              2303,\n",
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       "              2304,\n",
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       "              1192,\n",
       "              45,\n",
       "              377,\n",
       "              435,\n",
       "              94,\n",
       "              2008,\n",
       "              862],\n",
       "             734: [95,\n",
       "              1841,\n",
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       "              1006,\n",
       "              2197,\n",
       "              1388,\n",
       "              964,\n",
       "              408,\n",
       "              736,\n",
       "              2056,\n",
       "              751,\n",
       "              2202,\n",
       "              736],\n",
       "             735: [1958,\n",
       "              1881,\n",
       "              2060,\n",
       "              2061,\n",
       "              2062,\n",
       "              1237,\n",
       "              701,\n",
       "              739,\n",
       "              739,\n",
       "              1543,\n",
       "              1237],\n",
       "             736: [95, 734, 1841, 1006, 1631, 2197, 1388, 964, 734, 751, 2202],\n",
       "             737: [415, 1974, 1630, 88, 2136, 2178, 1269],\n",
       "             738: [1927, 2162, 1080, 405, 30],\n",
       "             739: [1958, 735, 1881, 701, 735, 1543, 1237, 393],\n",
       "             740: [1002, 2033, 141],\n",
       "             741: [2093, 1011, 1088, 1282, 831],\n",
       "             742: [1483, 1743, 1620],\n",
       "             743: [1986, 88, 745, 1239, 1570, 160],\n",
       "             744: [1358, 580, 1154, 223],\n",
       "             745: [1986, 1995, 366, 1127, 743, 160, 2009, 553],\n",
       "             746: [1303, 2006, 281],\n",
       "             747: [1538, 113, 282, 540, 282],\n",
       "             748: [1358,\n",
       "              1103,\n",
       "              1169,\n",
       "              274,\n",
       "              1617,\n",
       "              1550,\n",
       "              1732,\n",
       "              1568,\n",
       "              1374,\n",
       "              1145,\n",
       "              1145,\n",
       "              2553],\n",
       "             749: [2155, 274, 1333],\n",
       "             750: [1441],\n",
       "             751: [1204, 734, 736, 2198, 2202],\n",
       "             752: [957, 2083, 2451],\n",
       "             753: [1880, 1269],\n",
       "             754: [1358, 1483, 2450],\n",
       "             755: [1898, 2071, 1277],\n",
       "             756: [256,\n",
       "              2186,\n",
       "              2187,\n",
       "              433,\n",
       "              1469,\n",
       "              1472,\n",
       "              240,\n",
       "              1692,\n",
       "              885,\n",
       "              172,\n",
       "              512,\n",
       "              1692],\n",
       "             757: [1358, 2421, 1284],\n",
       "             758: [1358, 111, 111, 2492, 1762],\n",
       "             759: [1703, 733],\n",
       "             760: [2459, 567, 1513, 2460, 1426, 985],\n",
       "             761: [1401, 1443],\n",
       "             762: [2448, 859],\n",
       "             763: [1635, 707, 693],\n",
       "             764: [1358, 796, 1612, 1606],\n",
       "             765: [2367, 640, 1147],\n",
       "             766: [598, 316, 1297, 1868, 845],\n",
       "             767: [1701, 54, 873, 2314],\n",
       "             768: [1566, 1723, 1724],\n",
       "             769: [1927],\n",
       "             770: [2117, 1894],\n",
       "             771: [55, 1080, 65, 1156, 1156],\n",
       "             772: [908],\n",
       "             773: [1072, 1505],\n",
       "             774: [560],\n",
       "             775: [2075, 180, 171],\n",
       "             776: [1413, 1542, 402],\n",
       "             777: [702],\n",
       "             778: [1914, 1224, 1370, 779, 1919],\n",
       "             779: [1914, 1973, 1224, 702, 1370, 1592, 1919, 778],\n",
       "             780: [2341],\n",
       "             781: [2402, 218],\n",
       "             782: [245],\n",
       "             783: [1061, 2376, 638, 893, 1143],\n",
       "             784: [1701, 960],\n",
       "             785: [1664],\n",
       "             786: [947],\n",
       "             787: [438, 55, 325],\n",
       "             788: [1952, 2205, 1031, 2041, 2033],\n",
       "             789: [1703, 1240],\n",
       "             790: [1810, 482, 180, 171, 1548],\n",
       "             791: [2034, 2130, 180],\n",
       "             792: [1558, 2555, 1986, 218, 1488],\n",
       "             793: [1896, 1902, 1903, 2592],\n",
       "             794: [429, 1160, 733, 1590, 863],\n",
       "             795: [1810, 603, 1645],\n",
       "             796: [1358, 1103, 1317, 764],\n",
       "             797: [1358, 800, 1833, 73, 2359],\n",
       "             798: [1381, 1793, 1794, 1795],\n",
       "             799: [961],\n",
       "             800: [889, 797, 820, 1834],\n",
       "             801: [1470, 703, 1961, 2516],\n",
       "             802: [121, 1307],\n",
       "             803: [2100, 528],\n",
       "             804: [1307],\n",
       "             805: [275, 2236, 963, 706],\n",
       "             806: [403, 1383],\n",
       "             807: [661, 1955, 1226, 1956],\n",
       "             808: [638, 2383, 1785, 924],\n",
       "             809: [548, 2229, 266, 2228, 1115],\n",
       "             810: [1068],\n",
       "             811: [900, 855],\n",
       "             812: [1413, 1542, 507, 1300, 251],\n",
       "             813: [2376, 339],\n",
       "             814: [1158, 2382, 893, 2383],\n",
       "             815: [88, 2018, 55, 1344, 1174, 2017],\n",
       "             816: [436, 2405, 2282, 1842, 120, 483, 1980],\n",
       "             817: [2456, 221, 220, 90, 1736, 155, 156, 1763],\n",
       "             818: [415, 1999],\n",
       "             819: [1358, 650, 154, 364, 1606],\n",
       "             820: [889, 800],\n",
       "             821: [222],\n",
       "             822: [1973, 702],\n",
       "             823: [1358, 1169, 1765, 2221, 481],\n",
       "             824: [1831],\n",
       "             825: [1765],\n",
       "             826: [490, 2287, 610, 2528],\n",
       "             827: [1999, 1921, 1039, 324],\n",
       "             828: [1795, 444, 2464],\n",
       "             829: [1816],\n",
       "             830: [661, 1914, 2100],\n",
       "             831: [1358, 1638, 2093, 1011, 741, 136, 1733],\n",
       "             832: [2600],\n",
       "             833: [2036, 178, 207, 2495, 1641, 2595, 1678, 1130, 345, 1678],\n",
       "             834: [2168, 683, 131, 876],\n",
       "             835: [1810, 1121, 1134, 1654],\n",
       "             836: [519, 1572, 708, 1013, 2078, 1131, 1343, 2403],\n",
       "             837: [1422, 2670, 2248],\n",
       "             838: [868, 1131, 279, 270, 2280, 2280, 242],\n",
       "             839: [485, 2277, 965],\n",
       "             840: [2481, 1903],\n",
       "             841: [88, 2034],\n",
       "             842: [87, 161, 2016, 118],\n",
       "             843: [505, 548, 2339, 2542],\n",
       "             844: [1902, 472, 264, 264],\n",
       "             845: [598, 316, 766],\n",
       "             846: [2146, 374, 273],\n",
       "             847: [2189, 2422],\n",
       "             848: [1373, 985, 228],\n",
       "             849: [577, 2351, 394, 1993],\n",
       "             850: [1464, 2278, 712],\n",
       "             851: [88, 2018, 1309, 415],\n",
       "             852: [1800],\n",
       "             853: [1358, 1169, 1762],\n",
       "             854: [857, 344, 935, 470, 1097, 203, 1884, 1097, 203],\n",
       "             855: [2493, 811],\n",
       "             856: [2248, 1390],\n",
       "             857: [470, 1246, 854, 1097, 203],\n",
       "             858: [2182, 2502],\n",
       "             859: [487, 2096, 1030, 762, 1199],\n",
       "             860: [1427, 1527, 1758],\n",
       "             861: [95, 2330, 2068, 1397],\n",
       "             862: [733, 38, 38],\n",
       "             863: [429, 1160, 1590, 38, 794],\n",
       "             864: [2210, 104, 1065],\n",
       "             865: [2653],\n",
       "             866: [1049, 40],\n",
       "             867: [1229, 657, 2439, 2440, 2522, 1252, 2442, 871, 2523],\n",
       "             868: [988, 1341, 1195, 2276, 1844, 2099, 838, 1526],\n",
       "             869: [1701, 598, 232, 1440, 1864, 1864],\n",
       "             870: [1119, 2126, 577],\n",
       "             871: [1229, 657, 2530, 867, 2652],\n",
       "             872: [1413, 1542, 1340],\n",
       "             873: [1358, 261, 2313, 767, 1479, 1708],\n",
       "             874: [1701],\n",
       "             875: [310, 1945, 1950, 1942, 914],\n",
       "             876: [1358, 2168, 73, 2584, 558, 834],\n",
       "             877: [1413, 1542, 1177, 1176, 1935, 1300],\n",
       "             878: [436, 2326, 885],\n",
       "             879: [1558, 397],\n",
       "             880: [1013, 973],\n",
       "             881: [1199, 1155],\n",
       "             882: [1358],\n",
       "             883: [629, 609, 933, 227],\n",
       "             884: [89, 152],\n",
       "             885: [436, 651, 756, 878, 1039, 2386, 2024],\n",
       "             886: [622, 1400],\n",
       "             887: [1623, 1624, 306, 910, 239],\n",
       "             888: [1475, 1556, 614],\n",
       "             889: [800, 1830, 1831, 1832, 820],\n",
       "             890: [1269, 1314],\n",
       "             891: [645, 2608, 1674],\n",
       "             892: [310, 1950],\n",
       "             893: [638, 783, 911, 814, 1051, 2383, 2383],\n",
       "             894: [2367, 640, 1845],\n",
       "             895: [440, 35, 1187, 1296, 1913],\n",
       "             896: [465],\n",
       "             897: [1410, 1983, 146, 1907, 1156, 1152, 1494, 2295],\n",
       "             898: [1835, 92, 1836, 2160],\n",
       "             899: [1858, 1986, 297, 1055],\n",
       "             900: [639, 811],\n",
       "             901: [2186, 731, 1042, 2199, 2073, 1279],\n",
       "             902: [1358, 1284, 1604, 1604],\n",
       "             903: [2030, 2031, 446],\n",
       "             904: [541, 647, 1360, 1959, 379, 132, 1312],\n",
       "             905: [1483, 1282, 389, 1620],\n",
       "             906: [577, 2351, 2353],\n",
       "             907: [1351, 1916],\n",
       "             908: [1013, 772],\n",
       "             909: [445],\n",
       "             910: [1623, 139, 306, 887, 239, 2085],\n",
       "             911: [33, 2376, 893, 1534, 1051],\n",
       "             912: [2130],\n",
       "             913: [220],\n",
       "             914: [150, 875],\n",
       "             915: [1740, 1035, 2597, 2415],\n",
       "             916: [1026],\n",
       "             917: [2639],\n",
       "             918: [1542, 2065, 1098],\n",
       "             919: [1358],\n",
       "             920: [316, 1893],\n",
       "             921: [1914, 2134, 2293],\n",
       "             922: [1307, 1406],\n",
       "             923: [620],\n",
       "             924: [638, 2383, 808],\n",
       "             925: [1222],\n",
       "             926: [1862],\n",
       "             927: [2140, 1316, 17],\n",
       "             928: [327, 2063, 1326],\n",
       "             929: [1358, 2627],\n",
       "             930: [380, 2569, 477],\n",
       "             931: [1433],\n",
       "             932: [662],\n",
       "             933: [883, 534, 1038],\n",
       "             934: [94, 2356, 94],\n",
       "             935: [661, 973, 854, 451, 1873],\n",
       "             936: [1067, 2530, 246, 2515, 2515, 2641],\n",
       "             937: [2096, 1180, 1304, 1304],\n",
       "             938: [2230, 618, 2027],\n",
       "             939: [2173],\n",
       "             940: [1829],\n",
       "             941: [2517],\n",
       "             942: [1952, 1924],\n",
       "             943: [1196],\n",
       "             944: [2138],\n",
       "             945: [1072, 1911, 2388, 1512],\n",
       "             946: [1966, 2623],\n",
       "             947: [786],\n",
       "             948: [1395, 1681, 1682, 695],\n",
       "             949: [523],\n",
       "             950: [645, 437, 93],\n",
       "             951: [1358, 328],\n",
       "             952: [517, 2546],\n",
       "             953: [2565, 2566, 2567, 2565],\n",
       "             954: [1112, 677],\n",
       "             955: [1914, 175, 1482],\n",
       "             956: [2677, 492],\n",
       "             957: [1358, 1154, 752, 1557, 1685, 1757, 2167, 2083],\n",
       "             958: [1072, 306, 1798],\n",
       "             959: [2529],\n",
       "             960: [1776, 2650, 784],\n",
       "             961: [799, 2555, 1728, 2599],\n",
       "             962: [1806, 1062, 1665, 1807, 1808, 1809, 1810],\n",
       "             963: [1141,\n",
       "              29,\n",
       "              2399,\n",
       "              2400,\n",
       "              1785,\n",
       "              1417,\n",
       "              2240,\n",
       "              2401,\n",
       "              203,\n",
       "              1703,\n",
       "              375,\n",
       "              1157,\n",
       "              706,\n",
       "              1094,\n",
       "              258,\n",
       "              43,\n",
       "              1443,\n",
       "              805,\n",
       "              2434],\n",
       "             964: [1388, 257, 965, 734, 736, 2198],\n",
       "             965: [2197, 964, 1693, 839],\n",
       "             966: [415, 415],\n",
       "             967: [2659],\n",
       "             968: [1986, 598, 1603],\n",
       "             969: [1483, 1735, 704, 2450, 1743],\n",
       "             970: [1358, 2365, 16, 364, 466],\n",
       "             971: [107, 1650],\n",
       "             972: [2247, 1000, 2579, 2580],\n",
       "             973: [1072,\n",
       "              306,\n",
       "              671,\n",
       "              935,\n",
       "              880,\n",
       "              2153,\n",
       "              277,\n",
       "              2019,\n",
       "              1583,\n",
       "              115,\n",
       "              252,\n",
       "              630,\n",
       "              682,\n",
       "              1142,\n",
       "              2016,\n",
       "              176,\n",
       "              454],\n",
       "             974: [1496],\n",
       "             975: [2097],\n",
       "             976: [998, 1431],\n",
       "             977: [1281],\n",
       "             978: [1358, 998],\n",
       "             979: [524, 1303, 2207, 1503, 1957, 1839],\n",
       "             980: [1623, 1367, 121, 589],\n",
       "             981: [1221, 1159],\n",
       "             982: [2175, 2176, 1458, 1091, 1256],\n",
       "             983: [2130],\n",
       "             984: [543, 1068, 2265],\n",
       "             985: [1358, 1149, 1073, 848, 760],\n",
       "             986: [2697],\n",
       "             987: [1175],\n",
       "             988: [868],\n",
       "             989: [2285, 1645, 1507, 2436],\n",
       "             990: [1542, 310, 1054],\n",
       "             991: [307],\n",
       "             992: [596, 496],\n",
       "             993: [702, 2155],\n",
       "             994: [2309, 579, 1329, 1219],\n",
       "             995: [1309, 2385, 1912],\n",
       "             996: [2248, 2518, 368, 1257, 1135, 428],\n",
       "             997: [1837, 183, 182, 183],\n",
       "             998: [978, 976, 1103, 2365, 1431, 1284, 1431],\n",
       "             999: [1358, 346],\n",
       "             ...})"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[0., 0., 0., ..., 0., 0., 0.],\n",
       "        [0., 0., 0., ..., 0., 0., 0.],\n",
       "        [0., 0., 0., ..., 0., 0., 0.],\n",
       "        ...,\n",
       "        [0., 0., 0., ..., 0., 1., 0.],\n",
       "        [0., 0., 0., ..., 0., 0., 0.],\n",
       "        [0., 1., 0., ..., 0., 0., 0.]], dtype=float32)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.todense()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all(allx.todense()[:140,:] == x.todense()[:140, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "defaultdict(list,\n",
       "            {0: [633, 1862, 2582],\n",
       "             1: [2, 652, 654],\n",
       "             2: [1986, 332, 1666, 1, 1454],\n",
       "             3: [2544],\n",
       "             4: [2176, 1016, 2176, 1761, 1256, 2175],\n",
       "             5: [1629, 2546, 1659, 1659],\n",
       "             6: [1416, 1602, 1042, 373],\n",
       "             7: [208],\n",
       "             8: [281, 1996, 269],\n",
       "             9: [2614, 723, 723],\n",
       "             10: [476, 2545],\n",
       "             11: [1655, 1839],\n",
       "             12: [2661, 1001, 1318, 2662],\n",
       "             13: [1810, 1701],\n",
       "             14: [2034, 2075, 158, 2077, 2668],\n",
       "             15: [2367, 1093, 1090, 1271, 1093],\n",
       "             16: [2444, 1632, 970, 2642],\n",
       "             17: [24, 2140, 1316, 1315, 927],\n",
       "             18: [2082, 139, 1786, 1560, 2145],\n",
       "             19: [1939],\n",
       "             20: [1072, 2374, 2375, 2269, 2270],\n",
       "             21: [1043, 2310],\n",
       "             22: [1703, 1702, 2238, 39, 1234],\n",
       "             23: [2159],\n",
       "             24: [1701, 2139, 1636, 17, 2141, 598, 201],\n",
       "             25: [1344, 2011, 1301, 2317],\n",
       "             26: [2454, 2455, 123, 99, 122],\n",
       "             27: [1810, 606, 2360, 2578],\n",
       "             28: [1687],\n",
       "             29: [963, 2645],\n",
       "             30: [1358, 1416, 2162, 697, 2343, 738],\n",
       "             31: [1594],\n",
       "             32: [1973, 279, 518, 1850],\n",
       "             33: [2119, 911, 588, 1051, 2120, 286, 2040, 2121, 698],\n",
       "             34: [1358],\n",
       "             35: [1296, 1913, 895],\n",
       "             36: [1146, 1640, 1505, 2106, 1781, 2094, 1552, 2107],\n",
       "             37: [2427, 1190, 60],\n",
       "             38: [429, 1160, 862, 863, 862],\n",
       "             39: [1634, 1965, 1349, 1532, 1522, 22, 2357],\n",
       "             40: [507, 866, 1364],\n",
       "             41: [1914, 644, 175, 596],\n",
       "             42: [1372, 87],\n",
       "             43: [963, 2399, 2400, 152, 1653, 1530],\n",
       "             44: [1582, 2624, 2701, 2624],\n",
       "             45: [1986, 733, 2303, 1219, 2667, 2668],\n",
       "             46: [2366, 1604],\n",
       "             47: [1579, 163],\n",
       "             48: [598, 1666, 2471, 2205, 1031, 2041, 1662, 714, 2206],\n",
       "             49: [2034, 1666],\n",
       "             50: [1441],\n",
       "             51: [710, 2214, 2215, 2213, 457, 1392],\n",
       "             52: [1467, 2172, 2182, 1139, 1467, 2053],\n",
       "             53: [1358, 1103, 1739],\n",
       "             54: [767, 401],\n",
       "             55: [210,\n",
       "              1983,\n",
       "              787,\n",
       "              2020,\n",
       "              1156,\n",
       "              210,\n",
       "              771,\n",
       "              60,\n",
       "              815,\n",
       "              2021,\n",
       "              323,\n",
       "              651,\n",
       "              1079],\n",
       "             56: [1616, 412, 447, 1849],\n",
       "             57: [2418],\n",
       "             58: [1715],\n",
       "             59: [1358, 1725, 1627, 609, 615, 1287, 2651, 105, 580, 1067],\n",
       "             60: [55, 1527, 37],\n",
       "             61: [1416, 1309, 2162, 2312, 1080],\n",
       "             62: [485],\n",
       "             63: [1322],\n",
       "             64: [1737, 1209, 2616],\n",
       "             65: [1628,\n",
       "              2418,\n",
       "              2419,\n",
       "              543,\n",
       "              619,\n",
       "              1293,\n",
       "              1156,\n",
       "              771,\n",
       "              2418,\n",
       "              2021,\n",
       "              239],\n",
       "             66: [2631],\n",
       "             67: [540, 282, 2628],\n",
       "             68: [1358, 1986, 391],\n",
       "             69: [1013, 1914, 1926, 1351, 604, 1926, 1920, 2189],\n",
       "             70: [441, 2184],\n",
       "             71: [1986, 206, 2691, 2691],\n",
       "             72: [1358, 1103],\n",
       "             73: [1358,\n",
       "              797,\n",
       "              449,\n",
       "              1136,\n",
       "              558,\n",
       "              1723,\n",
       "              1189,\n",
       "              876,\n",
       "              1214,\n",
       "              1745,\n",
       "              1751,\n",
       "              1035,\n",
       "              1214],\n",
       "             74: [1416, 586, 1042, 2155, 544, 2419, 1118, 1517, 2052],\n",
       "             75: [2222, 2223, 2224, 2225, 84, 583],\n",
       "             76: [88, 2018, 2178],\n",
       "             77: [659, 1803],\n",
       "             78: [1418, 1329, 1219],\n",
       "             79: [2097, 603],\n",
       "             80: [257, 2049, 1117],\n",
       "             81: [2180, 347, 527, 423, 423],\n",
       "             82: [1634, 1138],\n",
       "             83: [1520, 2581],\n",
       "             84: [75, 2224, 284, 2223, 2226],\n",
       "             85: [1065, 2487, 2488],\n",
       "             86: [1336, 2034, 429, 2295],\n",
       "             87: [842, 2164, 42],\n",
       "             88: [2010,\n",
       "              130,\n",
       "              76,\n",
       "              2011,\n",
       "              1677,\n",
       "              2012,\n",
       "              2013,\n",
       "              1713,\n",
       "              1658,\n",
       "              1394,\n",
       "              1288,\n",
       "              498,\n",
       "              696,\n",
       "              1882,\n",
       "              851,\n",
       "              743,\n",
       "              2014,\n",
       "              1732,\n",
       "              162,\n",
       "              841,\n",
       "              1494,\n",
       "              1908,\n",
       "              1741,\n",
       "              1174,\n",
       "              1309,\n",
       "              300,\n",
       "              1527,\n",
       "              1847,\n",
       "              815,\n",
       "              2015,\n",
       "              2016,\n",
       "              2017,\n",
       "              1309,\n",
       "              415,\n",
       "              737,\n",
       "              2394,\n",
       "              2178],\n",
       "             89: [1087, 884, 1401, 2463, 1157, 1094, 258, 1653, 1530, 1585],\n",
       "             90: [1358, 817, 155, 156],\n",
       "             91: [2122, 2001, 330, 2001, 2380, 2123, 1046],\n",
       "             92: [898, 1836],\n",
       "             93: [2151, 550, 1495, 950],\n",
       "             94: [1966,\n",
       "              586,\n",
       "              733,\n",
       "              1649,\n",
       "              2490,\n",
       "              586,\n",
       "              195,\n",
       "              2355,\n",
       "              934,\n",
       "              2263,\n",
       "              2357,\n",
       "              934,\n",
       "              675],\n",
       "             95: [1535,\n",
       "              1838,\n",
       "              2200,\n",
       "              2201,\n",
       "              2197,\n",
       "              2199,\n",
       "              2181,\n",
       "              2054,\n",
       "              861,\n",
       "              334,\n",
       "              1303,\n",
       "              734,\n",
       "              736,\n",
       "              2074,\n",
       "              1628,\n",
       "              1602,\n",
       "              693,\n",
       "              456,\n",
       "              2183,\n",
       "              2182,\n",
       "              1580],\n",
       "             96: [2217],\n",
       "             97: [661, 1353],\n",
       "             98: [1521],\n",
       "             99: [123, 2454, 2455, 123, 122, 2604, 26],\n",
       "             100: [1602, 2056],\n",
       "             101: [1358, 281, 1589],\n",
       "             102: [1623, 109, 1878, 1448, 2256, 1251, 1871, 1561],\n",
       "             103: [139, 484, 306, 608, 1790, 1775],\n",
       "             104: [2210, 864, 401, 1065],\n",
       "             105: [1721, 59, 2651, 2476],\n",
       "             106: [2461],\n",
       "             107: [541, 1113, 971, 1650],\n",
       "             108: [2157, 1647, 2209],\n",
       "             109: [1624,\n",
       "              2045,\n",
       "              236,\n",
       "              306,\n",
       "              124,\n",
       "              1769,\n",
       "              289,\n",
       "              2092,\n",
       "              459,\n",
       "              318,\n",
       "              2093,\n",
       "              1772,\n",
       "              1045,\n",
       "              1785,\n",
       "              1337,\n",
       "              102,\n",
       "              1998,\n",
       "              1787,\n",
       "              610,\n",
       "              1789,\n",
       "              1779,\n",
       "              1346,\n",
       "              153,\n",
       "              519,\n",
       "              133,\n",
       "              1805,\n",
       "              426,\n",
       "              563,\n",
       "              2094,\n",
       "              176,\n",
       "              2095,\n",
       "              1661],\n",
       "             110: [1262, 567, 2279, 1161, 1599],\n",
       "             111: [1358, 1169, 2643, 758, 2492, 1762, 758],\n",
       "             112: [1623, 487, 306, 2080],\n",
       "             113: [540, 747, 1884],\n",
       "             114: [2288, 610, 2506],\n",
       "             115: [973],\n",
       "             116: [1076, 1501],\n",
       "             117: [259, 2537],\n",
       "             118: [1616,\n",
       "              388,\n",
       "              2010,\n",
       "              842,\n",
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       "              446,\n",
       "              255,\n",
       "              1343,\n",
       "              2165,\n",
       "              554,\n",
       "              581,\n",
       "              1690,\n",
       "              1507,\n",
       "              2112,\n",
       "              1029,\n",
       "              2166,\n",
       "              1538,\n",
       "              454,\n",
       "              1851],\n",
       "             119: [646, 1959, 379, 1549, 1901, 1537],\n",
       "             120: [514, 2405, 1842, 483, 816],\n",
       "             121: [1910, 980, 802, 1158, 2251, 589, 2252],\n",
       "             122: [2454, 2455, 99, 26],\n",
       "             123: [2455, 99, 2604, 99, 26],\n",
       "             124: [306, 109, 1367, 1622, 2478],\n",
       "             125: [458, 2363],\n",
       "             126: [1623, 2045, 236, 306, 1551, 2079],\n",
       "             127: [2604],\n",
       "             128: [233, 392, 370, 2270],\n",
       "             129: [441, 701],\n",
       "             130: [88, 2017, 1982],\n",
       "             131: [2169, 834],\n",
       "             132: [904, 1022, 1959, 379, 479],\n",
       "             133: [1623, 2045, 1670, 2082, 1777, 452, 399, 1784, 109],\n",
       "             134: [406],\n",
       "             135: [137, 2144, 2095],\n",
       "             136: [831],\n",
       "             137: [2144, 2329, 2504, 135],\n",
       "             138: [236, 306, 1776],\n",
       "             139: [1623, 660, 103, 1780, 910, 2045, 306, 18],\n",
       "             140: [582, 623, 582],\n",
       "             141: [2034, 1002, 740],\n",
       "             142: [2049, 1628, 525, 2181, 456],\n",
       "             143: [1701, 598, 316],\n",
       "             144: [2192, 1593, 145, 213],\n",
       "             145: [213, 537, 1593, 144, 1165, 2622],\n",
       "             146: [1927, 2059, 897, 1468, 1907],\n",
       "             147: [1976, 1519],\n",
       "             148: [714, 2518, 602, 714, 381, 378, 2518],\n",
       "             149: [1416, 2025, 1655, 1080],\n",
       "             150: [310, 1942, 914],\n",
       "             151: [1986, 2236, 2238, 2335],\n",
       "             152: [2238, 2240, 884, 43],\n",
       "             153: [1623, 2045, 236, 459, 306, 109],\n",
       "             154: [1358,\n",
       "              2525,\n",
       "              1444,\n",
       "              1339,\n",
       "              1238,\n",
       "              1568,\n",
       "              364,\n",
       "              326,\n",
       "              1752,\n",
       "              1753,\n",
       "              1754,\n",
       "              819],\n",
       "             155: [1358, 817, 1736, 90, 1689, 1763, 156],\n",
       "             156: [1358, 817, 90, 1689, 155, 1763],\n",
       "             157: [1701, 598, 1870, 2493],\n",
       "             158: [1701, 2034, 14, 180],\n",
       "             159: [2308, 180],\n",
       "             160: [1986, 745, 277, 743, 2000, 2009, 553],\n",
       "             161: [2010, 842],\n",
       "             162: [88, 323, 1667, 1174, 1268],\n",
       "             163: [47],\n",
       "             164: [210, 211],\n",
       "             165: [598, 1473, 2706, 2707],\n",
       "             166: [271, 2617],\n",
       "             167: [2437, 1056, 168, 2482],\n",
       "             168: [2437, 2438, 167],\n",
       "             169: [1994, 2706],\n",
       "             170: [1358, 1067],\n",
       "             171: [790, 1548, 775],\n",
       "             172: [756, 1692, 2187, 240, 512],\n",
       "             173: [1358, 687, 1033, 1586],\n",
       "             174: [1358, 1742, 629, 2334],\n",
       "             175: [1914, 2388, 955, 596, 41, 2217, 2135],\n",
       "             176: [109, 973, 231],\n",
       "             177: [2679, 2682, 1639, 726],\n",
       "             178: [833],\n",
       "             179: [1986, 231, 197],\n",
       "             180: [159, 2037, 1807, 1020, 2076, 791, 2004, 790, 775, 158],\n",
       "             181: [1013, 1464, 1359, 1683],\n",
       "             182: [183, 997],\n",
       "             183: [1837, 997, 182, 997],\n",
       "             184: [520],\n",
       "             185: [2003, 297],\n",
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       "             466: [1358, 2546, 970, 1738, 1305],\n",
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       "             472: [1825, 559, 448, 264, 844, 1183, 1182, 2029],\n",
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       "             482: [2230, 1812, 1814, 1807, 2307, 2308, 218, 790, 1810],\n",
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       "             484: [542, 2081, 2046, 1699, 103, 1367, 1775],\n",
       "             485: [1042, 839, 2219, 62],\n",
       "             486: [2077, 435, 2667, 2668],\n",
       "             487: [655,\n",
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       "              426,\n",
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       "             488: [444, 2547],\n",
       "             489: [1358, 2390, 2391],\n",
       "             490: [1973, 2105, 1879, 826, 2099, 1309, 1463, 1981, 1131],\n",
       "             491: [190],\n",
       "             492: [1257, 956, 1533, 688, 2678, 2673, 2538],\n",
       "             493: [1759, 1244, 391],\n",
       "             494: [2614],\n",
       "             495: [2192, 1328, 1327],\n",
       "             496: [711, 596, 992],\n",
       "             497: [2419],\n",
       "             498: [1652, 436, 437, 88, 323, 356],\n",
       "             499: [2457, 2458],\n",
       "             500: [2241],\n",
       "             501: [1358, 1765],\n",
       "             502: [279, 1976, 285],\n",
       "             503: [1692, 576, 2001],\n",
       "             504: [1973, 2394, 2396],\n",
       "             505: [573,\n",
       "              1180,\n",
       "              1304,\n",
       "              1448,\n",
       "              1258,\n",
       "              843,\n",
       "              1251,\n",
       "              1779,\n",
       "              1560,\n",
       "              2083,\n",
       "              406],\n",
       "             506: [1013, 1914, 1918, 1352],\n",
       "             507: [219,\n",
       "              1940,\n",
       "              1931,\n",
       "              1211,\n",
       "              1363,\n",
       "              1941,\n",
       "              402,\n",
       "              1933,\n",
       "              1413,\n",
       "              1176,\n",
       "              1300,\n",
       "              253,\n",
       "              254,\n",
       "              251,\n",
       "              812,\n",
       "              1936,\n",
       "              40,\n",
       "              2508],\n",
       "             508: [2325],\n",
       "             509: [1101, 2146, 2148],\n",
       "             510: [1013, 1131, 1171],\n",
       "             511: [1810, 549],\n",
       "             512: [756, 1472, 240, 1692, 172],\n",
       "             513: [565, 1528, 657],\n",
       "             514: [1978, 120, 1882, 1314, 478],\n",
       "             515: [444, 2464, 623, 2547, 2465, 1102, 1102],\n",
       "             516: [2104, 1882],\n",
       "             517: [2105, 952],\n",
       "             518: [666, 32, 2423, 1373],\n",
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       "              1574,\n",
       "              1670,\n",
       "              416,\n",
       "              836,\n",
       "              1998,\n",
       "              1986,\n",
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       "              598],\n",
       "             520: [184],\n",
       "             521: [598],\n",
       "             522: [2097],\n",
       "             523: [429, 949, 2406],\n",
       "             524: [1358, 979, 2476, 1169, 552],\n",
       "             525: [415,\n",
       "              1540,\n",
       "              2180,\n",
       "              2181,\n",
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       "              2182,\n",
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       "              456,\n",
       "              2183,\n",
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       "              2172,\n",
       "              2182],\n",
       "             526: [565, 1742, 1216, 1007],\n",
       "             527: [81, 423],\n",
       "             528: [803],\n",
       "             529: [1419, 1417, 2260, 2260],\n",
       "             530: [1013, 2094, 1505],\n",
       "             531: [606, 2308],\n",
       "             532: [1701, 1863],\n",
       "             533: [1742, 2466],\n",
       "             534: [629, 609, 933, 227],\n",
       "             535: [2641, 2392],\n",
       "             536: [1894, 567],\n",
       "             537: [2192, 1698, 1593, 145, 1165],\n",
       "             538: [1286],\n",
       "             539: [1616, 711, 2155],\n",
       "             540: [1441, 113, 67, 2527, 747],\n",
       "             541: [107, 904, 647, 1896, 1360, 1022],\n",
       "             542: [1623, 484, 306, 1245],\n",
       "             543: [984, 65],\n",
       "             544: [2199, 1769, 2347, 2052, 1580, 74, 399, 456],\n",
       "             545: [422],\n",
       "             546: [1608, 2127, 2127],\n",
       "             547: [1701, 598],\n",
       "             548: [2138, 809, 843, 1937, 1523],\n",
       "             549: [1810, 511, 1497, 230, 1810],\n",
       "             550: [93],\n",
       "             551: [231, 2388],\n",
       "             552: [1358, 1169, 524, 2201],\n",
       "             553: [1995, 366, 1127, 277, 745, 160, 1583, 2009],\n",
       "             554: [306, 118, 685],\n",
       "             555: [1463],\n",
       "             556: [1623, 1805],\n",
       "             557: [1725],\n",
       "             558: [73, 2585, 876, 1706, 1189],\n",
       "             559: [472, 1182, 1579],\n",
       "             560: [2526, 774],\n",
       "             561: [1016],\n",
       "             562: [1483, 1735, 704, 2450],\n",
       "             563: [1701, 2045, 109, 1337, 318, 1337],\n",
       "             564: [1262, 2476, 189],\n",
       "             565: [1398,\n",
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       "              244,\n",
       "              1361,\n",
       "              1610,\n",
       "              1723,\n",
       "              1528,\n",
       "              526,\n",
       "              2279,\n",
       "              1038,\n",
       "              427,\n",
       "              687,\n",
       "              1610],\n",
       "             566: [1986, 1907],\n",
       "             567: [760, 536, 1262, 631, 110, 290, 1513],\n",
       "             568: [1810, 1116, 1223, 1223],\n",
       "             569: [1759, 2512],\n",
       "             570: [201, 2430],\n",
       "             571: [696, 1570],\n",
       "             572: [1416, 2025, 2418],\n",
       "             573: [505, 306, 643, 1313, 2407],\n",
       "             574: [1692, 576, 2001],\n",
       "             575: [2283],\n",
       "             576: [1810, 665, 2348, 503, 574, 665],\n",
       "             577: [1518,\n",
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       "              230,\n",
       "              906,\n",
       "              2351,\n",
       "              2352,\n",
       "              2353,\n",
       "              2354,\n",
       "              394,\n",
       "              849,\n",
       "              1063,\n",
       "              1129],\n",
       "             578: [266, 1879, 1974, 1105],\n",
       "             579: [1808, 994, 1134],\n",
       "             580: [1358, 744, 2444, 1742, 2445, 1758, 1765, 59],\n",
       "             581: [1623, 1792, 1616, 306, 118, 454],\n",
       "             582: [444, 140, 140, 2548, 2549],\n",
       "             583: [75, 2224, 284, 2224, 2225],\n",
       "             584: [340, 623, 2463, 2289, 2464],\n",
       "             585: [2526],\n",
       "             586: [1224, 1218, 74, 94, 2155, 94],\n",
       "             587: [1032, 1032],\n",
       "             588: [33, 442, 2383, 698],\n",
       "             589: [1624, 121, 1158, 980],\n",
       "             590: [1954, 1441],\n",
       "             591: [1423, 1017, 1078, 2472, 642],\n",
       "             592: [2669],\n",
       "             593: [415, 1115, 1474],\n",
       "             594: [2195, 663],\n",
       "             595: [2176, 1016, 1256],\n",
       "             596: [1914, 644, 175, 496, 992, 41],\n",
       "             597: [1628, 1104],\n",
       "             598: [157,\n",
       "              547,\n",
       "              1003,\n",
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       "              316,\n",
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       "              1864,\n",
       "              1821,\n",
       "              201,\n",
       "              519,\n",
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       "              297,\n",
       "              1297,\n",
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       "              48,\n",
       "              1823,\n",
       "              1636,\n",
       "              24,\n",
       "              1301,\n",
       "              1870,\n",
       "              1473,\n",
       "              1573,\n",
       "              1875,\n",
       "              1100,\n",
       "              165,\n",
       "              2707,\n",
       "              1473],\n",
       "             599: [1271, 1093],\n",
       "             600: [2394],\n",
       "             601: [2229],\n",
       "             602: [148, 378],\n",
       "             603: [2045, 716, 1248, 795, 1821, 79, 1873],\n",
       "             604: [1914, 1652, 1351, 69, 2109],\n",
       "             605: [1107, 2534],\n",
       "             606: [2230, 2360, 1666, 531, 27, 2361],\n",
       "             607: [1213, 1664, 298],\n",
       "             608: [1623, 306, 103, 191, 2080],\n",
       "             609: [1358, 2446, 59, 883, 534, 1041, 2447, 2448],\n",
       "             610: [109, 2287, 2288, 826, 234, 2481, 114],\n",
       "             611: [2690],\n",
       "             612: [2235],\n",
       "             613: [1358, 341],\n",
       "             614: [1475, 2470, 2470, 888],\n",
       "             615: [59, 2443],\n",
       "             616: [1358, 2365, 1739, 2503],\n",
       "             617: [2034, 705],\n",
       "             618: [288, 938],\n",
       "             619: [65, 239],\n",
       "             620: [469, 2534, 923],\n",
       "             621: [2018, 1332, 249, 1978],\n",
       "             622: [1951, 1952, 1002, 886],\n",
       "             623: [444, 584, 2464, 2289, 140, 515],\n",
       "             624: [1042, 1232],\n",
       "             625: [1024],\n",
       "             626: [1358, 372, 2556, 2558],\n",
       "             627: [2122, 2238, 2335, 442],\n",
       "             628: [1764, 1169, 2546, 1725],\n",
       "             629: [174, 883, 534],\n",
       "             630: [973],\n",
       "             631: [567, 2358],\n",
       "             632: [1430],\n",
       "             633: [1701, 0, 1866],\n",
       "             634: [2227, 300],\n",
       "             635: [2058],\n",
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       "             639: [900],\n",
       "             640: [2420, 395, 894, 765, 1090, 1598],\n",
       "             641: [2704],\n",
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       "             643: [1538, 573, 1167, 2407],\n",
       "             644: [711, 728, 2177, 596, 41, 1258],\n",
       "             645: [1358,\n",
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       "              1898,\n",
       "              1899,\n",
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       "              1900,\n",
       "              1495,\n",
       "              950,\n",
       "              1895,\n",
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       "              1901,\n",
       "              1826],\n",
       "             646: [119],\n",
       "             647: [468, 1267, 541, 904, 1360],\n",
       "             648: [1441],\n",
       "             649: [1171, 1457],\n",
       "             650: [1250, 1486, 1557, 1685, 1756, 819, 2083],\n",
       "             651: [2023, 1984, 55, 885, 2024, 1667, 2156],\n",
       "             652: [470, 1],\n",
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       "             654: [1],\n",
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       "              871,\n",
       "              2523,\n",
       "              1729],\n",
       "             658: [2147],\n",
       "             659: [77, 354, 1803],\n",
       "             660: [1623, 139],\n",
       "             661: [1353,\n",
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       "              1028,\n",
       "              935,\n",
       "              1879,\n",
       "              1880,\n",
       "              830,\n",
       "              1881,\n",
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       "              1045,\n",
       "              1882,\n",
       "              1883,\n",
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       "              1884,\n",
       "              1885],\n",
       "             662: [932],\n",
       "             663: [2195, 594],\n",
       "             664: [1701],\n",
       "             665: [397, 2120, 576, 2122, 576, 332],\n",
       "             666: [1973, 279, 518, 1850],\n",
       "             667: [2364, 456, 2472],\n",
       "             668: [436],\n",
       "             669: [729, 1086, 1124],\n",
       "             670: [267, 2606],\n",
       "             671: [2025, 441, 973, 451],\n",
       "             672: [2456, 376],\n",
       "             673: [1986, 1907],\n",
       "             674: [1907],\n",
       "             675: [2356, 94],\n",
       "             676: [1955, 2235, 410],\n",
       "             677: [954],\n",
       "             678: [733, 377],\n",
       "             679: [1395],\n",
       "             680: [2199],\n",
       "             681: [1986, 1445, 1446, 1171, 1445, 1446],\n",
       "             682: [1224, 973],\n",
       "             683: [2169, 834],\n",
       "             684: [1358, 1282],\n",
       "             685: [554],\n",
       "             686: [1358, 2366],\n",
       "             687: [1358,\n",
       "              1171,\n",
       "              1710,\n",
       "              1033,\n",
       "              1586,\n",
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       "              480,\n",
       "              173,\n",
       "              2359,\n",
       "              1546,\n",
       "              2372,\n",
       "              290,\n",
       "              1721],\n",
       "             688: [1257, 492],\n",
       "             689: [1358, 1317, 1169, 1721, 1292],\n",
       "             690: [311],\n",
       "             691: [2034, 2130],\n",
       "             692: [2629],\n",
       "             693: [2108, 763, 95, 1851, 334],\n",
       "             694: [1478, 2516],\n",
       "             695: [1336, 1681, 1682, 1998, 2319, 1012, 1790, 407, 948],\n",
       "             696: [88, 277, 571, 1570],\n",
       "             697: [30, 1080],\n",
       "             698: [33, 1015, 442, 588, 286],\n",
       "             699: [1701, 2045, 2327],\n",
       "             700: [1691],\n",
       "             701: [735, 739, 129, 2062],\n",
       "             702: [777, 993, 1637, 2101, 1368, 822, 779, 2069, 2070],\n",
       "             703: [2497, 1961, 801],\n",
       "             704: [1483, 969, 562, 389, 2450, 1743, 1412, 2113, 2113],\n",
       "             705: [429, 617],\n",
       "             706: [1240, 2238, 963, 805, 2645],\n",
       "             707: [763],\n",
       "             708: [1358, 2212, 2216, 836],\n",
       "             709: [1896, 1903],\n",
       "             710: [51, 2212, 2213, 1392],\n",
       "             711: [2111, 1285, 496, 539, 252, 414, 2112, 2113, 644],\n",
       "             712: [1464, 850, 2480],\n",
       "             713: [1044],\n",
       "             714: [1385, 148, 148, 48],\n",
       "             715: [2291],\n",
       "             716: [1810, 603, 1821, 2409],\n",
       "             717: [1907],\n",
       "             718: [1416, 438, 437, 2059, 2261],\n",
       "             719: [1623, 1810, 306, 302, 303],\n",
       "             720: [1441, 392, 371],\n",
       "             721: [1034],\n",
       "             722: [1273, 1874, 2500, 1567, 2501, 1567],\n",
       "             723: [2614, 9, 9],\n",
       "             724: [1344, 2394, 2395],\n",
       "             725: [1652, 2071, 440, 1104, 1137],\n",
       "             726: [2671, 1533, 177],\n",
       "             727: [1386, 2570],\n",
       "             728: [1296, 644, 2388, 2553, 1070],\n",
       "             729: [1701, 2534, 1221, 1159, 669],\n",
       "             730: [398],\n",
       "             731: [901, 2199, 1279, 2203],\n",
       "             732: [364, 1756, 2685, 296, 263],\n",
       "             733: [2035,\n",
       "              1062,\n",
       "              1265,\n",
       "              2011,\n",
       "              2301,\n",
       "              2302,\n",
       "              1329,\n",
       "              759,\n",
       "              1817,\n",
       "              678,\n",
       "              1294,\n",
       "              1818,\n",
       "              401,\n",
       "              2303,\n",
       "              383,\n",
       "              1160,\n",
       "              2304,\n",
       "              218,\n",
       "              2291,\n",
       "              794,\n",
       "              1682,\n",
       "              2268,\n",
       "              1192,\n",
       "              45,\n",
       "              377,\n",
       "              435,\n",
       "              94,\n",
       "              2008,\n",
       "              862],\n",
       "             734: [95,\n",
       "              1841,\n",
       "              2277,\n",
       "              1006,\n",
       "              2197,\n",
       "              1388,\n",
       "              964,\n",
       "              408,\n",
       "              736,\n",
       "              2056,\n",
       "              751,\n",
       "              2202,\n",
       "              736],\n",
       "             735: [1958,\n",
       "              1881,\n",
       "              2060,\n",
       "              2061,\n",
       "              2062,\n",
       "              1237,\n",
       "              701,\n",
       "              739,\n",
       "              739,\n",
       "              1543,\n",
       "              1237],\n",
       "             736: [95, 734, 1841, 1006, 1631, 2197, 1388, 964, 734, 751, 2202],\n",
       "             737: [415, 1974, 1630, 88, 2136, 2178, 1269],\n",
       "             738: [1927, 2162, 1080, 405, 30],\n",
       "             739: [1958, 735, 1881, 701, 735, 1543, 1237, 393],\n",
       "             740: [1002, 2033, 141],\n",
       "             741: [2093, 1011, 1088, 1282, 831],\n",
       "             742: [1483, 1743, 1620],\n",
       "             743: [1986, 88, 745, 1239, 1570, 160],\n",
       "             744: [1358, 580, 1154, 223],\n",
       "             745: [1986, 1995, 366, 1127, 743, 160, 2009, 553],\n",
       "             746: [1303, 2006, 281],\n",
       "             747: [1538, 113, 282, 540, 282],\n",
       "             748: [1358,\n",
       "              1103,\n",
       "              1169,\n",
       "              274,\n",
       "              1617,\n",
       "              1550,\n",
       "              1732,\n",
       "              1568,\n",
       "              1374,\n",
       "              1145,\n",
       "              1145,\n",
       "              2553],\n",
       "             749: [2155, 274, 1333],\n",
       "             750: [1441],\n",
       "             751: [1204, 734, 736, 2198, 2202],\n",
       "             752: [957, 2083, 2451],\n",
       "             753: [1880, 1269],\n",
       "             754: [1358, 1483, 2450],\n",
       "             755: [1898, 2071, 1277],\n",
       "             756: [256,\n",
       "              2186,\n",
       "              2187,\n",
       "              433,\n",
       "              1469,\n",
       "              1472,\n",
       "              240,\n",
       "              1692,\n",
       "              885,\n",
       "              172,\n",
       "              512,\n",
       "              1692],\n",
       "             757: [1358, 2421, 1284],\n",
       "             758: [1358, 111, 111, 2492, 1762],\n",
       "             759: [1703, 733],\n",
       "             760: [2459, 567, 1513, 2460, 1426, 985],\n",
       "             761: [1401, 1443],\n",
       "             762: [2448, 859],\n",
       "             763: [1635, 707, 693],\n",
       "             764: [1358, 796, 1612, 1606],\n",
       "             765: [2367, 640, 1147],\n",
       "             766: [598, 316, 1297, 1868, 845],\n",
       "             767: [1701, 54, 873, 2314],\n",
       "             768: [1566, 1723, 1724],\n",
       "             769: [1927],\n",
       "             770: [2117, 1894],\n",
       "             771: [55, 1080, 65, 1156, 1156],\n",
       "             772: [908],\n",
       "             773: [1072, 1505],\n",
       "             774: [560],\n",
       "             775: [2075, 180, 171],\n",
       "             776: [1413, 1542, 402],\n",
       "             777: [702],\n",
       "             778: [1914, 1224, 1370, 779, 1919],\n",
       "             779: [1914, 1973, 1224, 702, 1370, 1592, 1919, 778],\n",
       "             780: [2341],\n",
       "             781: [2402, 218],\n",
       "             782: [245],\n",
       "             783: [1061, 2376, 638, 893, 1143],\n",
       "             784: [1701, 960],\n",
       "             785: [1664],\n",
       "             786: [947],\n",
       "             787: [438, 55, 325],\n",
       "             788: [1952, 2205, 1031, 2041, 2033],\n",
       "             789: [1703, 1240],\n",
       "             790: [1810, 482, 180, 171, 1548],\n",
       "             791: [2034, 2130, 180],\n",
       "             792: [1558, 2555, 1986, 218, 1488],\n",
       "             793: [1896, 1902, 1903, 2592],\n",
       "             794: [429, 1160, 733, 1590, 863],\n",
       "             795: [1810, 603, 1645],\n",
       "             796: [1358, 1103, 1317, 764],\n",
       "             797: [1358, 800, 1833, 73, 2359],\n",
       "             798: [1381, 1793, 1794, 1795],\n",
       "             799: [961],\n",
       "             800: [889, 797, 820, 1834],\n",
       "             801: [1470, 703, 1961, 2516],\n",
       "             802: [121, 1307],\n",
       "             803: [2100, 528],\n",
       "             804: [1307],\n",
       "             805: [275, 2236, 963, 706],\n",
       "             806: [403, 1383],\n",
       "             807: [661, 1955, 1226, 1956],\n",
       "             808: [638, 2383, 1785, 924],\n",
       "             809: [548, 2229, 266, 2228, 1115],\n",
       "             810: [1068],\n",
       "             811: [900, 855],\n",
       "             812: [1413, 1542, 507, 1300, 251],\n",
       "             813: [2376, 339],\n",
       "             814: [1158, 2382, 893, 2383],\n",
       "             815: [88, 2018, 55, 1344, 1174, 2017],\n",
       "             816: [436, 2405, 2282, 1842, 120, 483, 1980],\n",
       "             817: [2456, 221, 220, 90, 1736, 155, 156, 1763],\n",
       "             818: [415, 1999],\n",
       "             819: [1358, 650, 154, 364, 1606],\n",
       "             820: [889, 800],\n",
       "             821: [222],\n",
       "             822: [1973, 702],\n",
       "             823: [1358, 1169, 1765, 2221, 481],\n",
       "             824: [1831],\n",
       "             825: [1765],\n",
       "             826: [490, 2287, 610, 2528],\n",
       "             827: [1999, 1921, 1039, 324],\n",
       "             828: [1795, 444, 2464],\n",
       "             829: [1816],\n",
       "             830: [661, 1914, 2100],\n",
       "             831: [1358, 1638, 2093, 1011, 741, 136, 1733],\n",
       "             832: [2600],\n",
       "             833: [2036, 178, 207, 2495, 1641, 2595, 1678, 1130, 345, 1678],\n",
       "             834: [2168, 683, 131, 876],\n",
       "             835: [1810, 1121, 1134, 1654],\n",
       "             836: [519, 1572, 708, 1013, 2078, 1131, 1343, 2403],\n",
       "             837: [1422, 2670, 2248],\n",
       "             838: [868, 1131, 279, 270, 2280, 2280, 242],\n",
       "             839: [485, 2277, 965],\n",
       "             840: [2481, 1903],\n",
       "             841: [88, 2034],\n",
       "             842: [87, 161, 2016, 118],\n",
       "             843: [505, 548, 2339, 2542],\n",
       "             844: [1902, 472, 264, 264],\n",
       "             845: [598, 316, 766],\n",
       "             846: [2146, 374, 273],\n",
       "             847: [2189, 2422],\n",
       "             848: [1373, 985, 228],\n",
       "             849: [577, 2351, 394, 1993],\n",
       "             850: [1464, 2278, 712],\n",
       "             851: [88, 2018, 1309, 415],\n",
       "             852: [1800],\n",
       "             853: [1358, 1169, 1762],\n",
       "             854: [857, 344, 935, 470, 1097, 203, 1884, 1097, 203],\n",
       "             855: [2493, 811],\n",
       "             856: [2248, 1390],\n",
       "             857: [470, 1246, 854, 1097, 203],\n",
       "             858: [2182, 2502],\n",
       "             859: [487, 2096, 1030, 762, 1199],\n",
       "             860: [1427, 1527, 1758],\n",
       "             861: [95, 2330, 2068, 1397],\n",
       "             862: [733, 38, 38],\n",
       "             863: [429, 1160, 1590, 38, 794],\n",
       "             864: [2210, 104, 1065],\n",
       "             865: [2653],\n",
       "             866: [1049, 40],\n",
       "             867: [1229, 657, 2439, 2440, 2522, 1252, 2442, 871, 2523],\n",
       "             868: [988, 1341, 1195, 2276, 1844, 2099, 838, 1526],\n",
       "             869: [1701, 598, 232, 1440, 1864, 1864],\n",
       "             870: [1119, 2126, 577],\n",
       "             871: [1229, 657, 2530, 867, 2652],\n",
       "             872: [1413, 1542, 1340],\n",
       "             873: [1358, 261, 2313, 767, 1479, 1708],\n",
       "             874: [1701],\n",
       "             875: [310, 1945, 1950, 1942, 914],\n",
       "             876: [1358, 2168, 73, 2584, 558, 834],\n",
       "             877: [1413, 1542, 1177, 1176, 1935, 1300],\n",
       "             878: [436, 2326, 885],\n",
       "             879: [1558, 397],\n",
       "             880: [1013, 973],\n",
       "             881: [1199, 1155],\n",
       "             882: [1358],\n",
       "             883: [629, 609, 933, 227],\n",
       "             884: [89, 152],\n",
       "             885: [436, 651, 756, 878, 1039, 2386, 2024],\n",
       "             886: [622, 1400],\n",
       "             887: [1623, 1624, 306, 910, 239],\n",
       "             888: [1475, 1556, 614],\n",
       "             889: [800, 1830, 1831, 1832, 820],\n",
       "             890: [1269, 1314],\n",
       "             891: [645, 2608, 1674],\n",
       "             892: [310, 1950],\n",
       "             893: [638, 783, 911, 814, 1051, 2383, 2383],\n",
       "             894: [2367, 640, 1845],\n",
       "             895: [440, 35, 1187, 1296, 1913],\n",
       "             896: [465],\n",
       "             897: [1410, 1983, 146, 1907, 1156, 1152, 1494, 2295],\n",
       "             898: [1835, 92, 1836, 2160],\n",
       "             899: [1858, 1986, 297, 1055],\n",
       "             900: [639, 811],\n",
       "             901: [2186, 731, 1042, 2199, 2073, 1279],\n",
       "             902: [1358, 1284, 1604, 1604],\n",
       "             903: [2030, 2031, 446],\n",
       "             904: [541, 647, 1360, 1959, 379, 132, 1312],\n",
       "             905: [1483, 1282, 389, 1620],\n",
       "             906: [577, 2351, 2353],\n",
       "             907: [1351, 1916],\n",
       "             908: [1013, 772],\n",
       "             909: [445],\n",
       "             910: [1623, 139, 306, 887, 239, 2085],\n",
       "             911: [33, 2376, 893, 1534, 1051],\n",
       "             912: [2130],\n",
       "             913: [220],\n",
       "             914: [150, 875],\n",
       "             915: [1740, 1035, 2597, 2415],\n",
       "             916: [1026],\n",
       "             917: [2639],\n",
       "             918: [1542, 2065, 1098],\n",
       "             919: [1358],\n",
       "             920: [316, 1893],\n",
       "             921: [1914, 2134, 2293],\n",
       "             922: [1307, 1406],\n",
       "             923: [620],\n",
       "             924: [638, 2383, 808],\n",
       "             925: [1222],\n",
       "             926: [1862],\n",
       "             927: [2140, 1316, 17],\n",
       "             928: [327, 2063, 1326],\n",
       "             929: [1358, 2627],\n",
       "             930: [380, 2569, 477],\n",
       "             931: [1433],\n",
       "             932: [662],\n",
       "             933: [883, 534, 1038],\n",
       "             934: [94, 2356, 94],\n",
       "             935: [661, 973, 854, 451, 1873],\n",
       "             936: [1067, 2530, 246, 2515, 2515, 2641],\n",
       "             937: [2096, 1180, 1304, 1304],\n",
       "             938: [2230, 618, 2027],\n",
       "             939: [2173],\n",
       "             940: [1829],\n",
       "             941: [2517],\n",
       "             942: [1952, 1924],\n",
       "             943: [1196],\n",
       "             944: [2138],\n",
       "             945: [1072, 1911, 2388, 1512],\n",
       "             946: [1966, 2623],\n",
       "             947: [786],\n",
       "             948: [1395, 1681, 1682, 695],\n",
       "             949: [523],\n",
       "             950: [645, 437, 93],\n",
       "             951: [1358, 328],\n",
       "             952: [517, 2546],\n",
       "             953: [2565, 2566, 2567, 2565],\n",
       "             954: [1112, 677],\n",
       "             955: [1914, 175, 1482],\n",
       "             956: [2677, 492],\n",
       "             957: [1358, 1154, 752, 1557, 1685, 1757, 2167, 2083],\n",
       "             958: [1072, 306, 1798],\n",
       "             959: [2529],\n",
       "             960: [1776, 2650, 784],\n",
       "             961: [799, 2555, 1728, 2599],\n",
       "             962: [1806, 1062, 1665, 1807, 1808, 1809, 1810],\n",
       "             963: [1141,\n",
       "              29,\n",
       "              2399,\n",
       "              2400,\n",
       "              1785,\n",
       "              1417,\n",
       "              2240,\n",
       "              2401,\n",
       "              203,\n",
       "              1703,\n",
       "              375,\n",
       "              1157,\n",
       "              706,\n",
       "              1094,\n",
       "              258,\n",
       "              43,\n",
       "              1443,\n",
       "              805,\n",
       "              2434],\n",
       "             964: [1388, 257, 965, 734, 736, 2198],\n",
       "             965: [2197, 964, 1693, 839],\n",
       "             966: [415, 415],\n",
       "             967: [2659],\n",
       "             968: [1986, 598, 1603],\n",
       "             969: [1483, 1735, 704, 2450, 1743],\n",
       "             970: [1358, 2365, 16, 364, 466],\n",
       "             971: [107, 1650],\n",
       "             972: [2247, 1000, 2579, 2580],\n",
       "             973: [1072,\n",
       "              306,\n",
       "              671,\n",
       "              935,\n",
       "              880,\n",
       "              2153,\n",
       "              277,\n",
       "              2019,\n",
       "              1583,\n",
       "              115,\n",
       "              252,\n",
       "              630,\n",
       "              682,\n",
       "              1142,\n",
       "              2016,\n",
       "              176,\n",
       "              454],\n",
       "             974: [1496],\n",
       "             975: [2097],\n",
       "             976: [998, 1431],\n",
       "             977: [1281],\n",
       "             978: [1358, 998],\n",
       "             979: [524, 1303, 2207, 1503, 1957, 1839],\n",
       "             980: [1623, 1367, 121, 589],\n",
       "             981: [1221, 1159],\n",
       "             982: [2175, 2176, 1458, 1091, 1256],\n",
       "             983: [2130],\n",
       "             984: [543, 1068, 2265],\n",
       "             985: [1358, 1149, 1073, 848, 760],\n",
       "             986: [2697],\n",
       "             987: [1175],\n",
       "             988: [868],\n",
       "             989: [2285, 1645, 1507, 2436],\n",
       "             990: [1542, 310, 1054],\n",
       "             991: [307],\n",
       "             992: [596, 496],\n",
       "             993: [702, 2155],\n",
       "             994: [2309, 579, 1329, 1219],\n",
       "             995: [1309, 2385, 1912],\n",
       "             996: [2248, 2518, 368, 1257, 1135, 428],\n",
       "             997: [1837, 183, 182, 183],\n",
       "             998: [978, 976, 1103, 2365, 1431, 1284, 1431],\n",
       "             999: [1358, 346],\n",
       "             ...})"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.32317763436\n"
     ]
    }
   ],
   "source": [
    "G = nx.from_dict_of_lists(graph)\n",
    "pair_count = 0; dist_count = 0\n",
    "for S in nx.connected_component_subgraphs(G):\n",
    "    count = len(S.nodes) * (len(S.nodes) - 1)\n",
    "    dist = nx.average_shortest_path_length(S) * count\n",
    "    dist_count += dist; pair_count += count\n",
    "print(dist_count / pair_count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2708"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "nx.con"
   ]
  }
 ],
 "metadata": {
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   "display_name": "python27",
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   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15"
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 },
 "nbformat": 4,
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